Is the current emperor of Japan the true and legitimate emperor?
From 1333 to 1336, the emperor Go-Daigo attempted to reassert imperial authority against the Kamakura Shogun. This was called the Kenmu Restoration. The conflict between Go-Daigo and the shogunate centered on succession to the imperial throne. Whereas Go-Daigo demanded the authority to name his own heir, the shogunate insisted on maintaining a 13th century compromise whereby two rival branches of the imperial line would succeed to the throne in turn.
Go-Daigo refused to compromise, and in 1331 he launched a coup against the shogunate. The coup failed and Go-Daigo was sent into internal exile. Go-Daigo's warrior supporters reorganized and destroyed the shogunate in 1333. Once in power however, Go-Daigo showed little appreciation for his warrior allies. In the name of imperial rule he sought to strengthen central control at the expense of the regional authority of the warrior class.
In a striking miscalculation he named as shogun his own son, slighting the generals who had restored him to the throne. This disregard for warrior privilege alienated Go-Daigo's supporters and undermined his government. In 1335, Ashikaga Takauji, one of Go-Daigo's allies, drove him from Kyoto and installed as emperor a member of the rival lineage. Three years later Takauji arranged his own appointment as shogun, founding the Ashikaga shogunate, the 2nd of Japan's three shogun dynasties.
Go-Daigo continued to have supporters who defended his imperial line, known as the Southern Court and they fought against the Ashikaga shogunate. The imperial succession dispute was resolved in 1392, but the resolution represented a victory for the Northern Court. The two lines again agreed to alternate succession, but in practice the Northern line never relinquished control.
The current Japanese emperor descends from the Northern Court. The Southern Court effectively vanished.
(The Last Samurai-The Life and Times of Saigo Takamori)